Mrs. Figg is the "mad old lady" to whose house Harry goes once a year on Dudley's birthday. Harry hates it there. Her house smells like cabbage and Mrs. Figg always makes him look at pictures of every cat she ever owned. JKR has stated that she is the same person as the Arabella Figg mentioned as being part of the "old crowd" (GF36) and that we will learn more about her in book 5 (BP). Many fans had already made that connection. So how did fans figure out that Mrs. Figg and Arabella Figg were one and the same? Here are some of the clues that support that idea:

• It is stated several times that Harry is protected when he's at the Dursley's house. Is part of that protection a few faithful magic folk who have spent the last ten or eleven years living as Muggles near Privet Drive in order to watch over Harry? Mrs. Figg lives just two streets away.
• When Harry is locked in his cupboard for his longest punishment ever, he comes out to discover that Dudley had "knocked down old Mrs. Figg as she crossed Privet Drive on her crutches." But Mrs. Figg lives two streets away. What wasshe doing on Privet Drive on crutches, with a broken leg? Checking on Harry? After all, he'd just vanished for weeks and she was bound to start wondering where he'd been. But the Dursleys tried to hide Harry from the world, didn't they? So would she expect to see Harry outside? Yep, because he spent as much time as he could outside of the house to avoid Dudley and his gang. She would expect to be able to see Harry every single day, since the mean boys came over every day. 
• How did she break her leg? What battles with evil took place outside of Harry's sight, maybe just a few streets away? She supposedly fell over one of her cats and subsequently wasn't as fond of them as she used to be. Did one of them turn out to be an enemy?
• Speaking of the cats, were they perhaps acting as spies for her? Okay, there isn't much evidence of that, except maybe for the fact that he looks out of the window and as far as Harry can see through the darkness, there isn't a living creature in sight, "not even a cat." (GF2) Is that unusual? Would he often see cats skulking about Privet Drive at night, so often that when he doesn't see one, it strikes him as slightly unusual?
• Arthur Weasley borrows a magic tent for them from Perkins, an "old warlock" who works with him at the Ministry. To Harry's surprise, it's furnished in exactly the same sort of style as Mrs. Figg's house; it even smelled strongly of cats. Is this style sort of the standard pseudo-Muggle style used for any imitation Muggle dwelling? And therefore, was Mrs. Figg's house also a wizard imitation of a Muggle house?
• Lastly, think about Harry's sudden escape from Privet Drive after "blowing up" Aunt Marge. He ends up, according to PA, several streets away, on Magnolia Crescent. Remember that Mrs. Figg lives two streets away. Could it be that he ended up at the edge of his "safe zone"? Sirius was there, watching him...had Sirius been stopped at the edge coming in? And it was a few seconds later that the Knight Bus appeared out of nowhere, supposedly because Harry held up his wand. Okay, he did, that's true, but the Knight Bus is supposed to stop for you if you hold up you wand intentionally for that purpose. Harry did no such thing. His wand was up completely by accident. So who really called the Knight Bus for Harry? Was it Mrs. Figg or perhaps another witch or wizard who lived along the perimeter?